Finite Horizon H∞ and Related Control Problems

Subrahmanyam, M. B.

doi:10.1007/978-1-4612-4272-7

Cited by 11 publications

(10 citation statements)

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“…And even the kind of mobility that we might think of as strictly commercial had an enormous effect on the flow of ideas and cultural capital, as the rise of new early modern merchant classes also created new patronage networks that became, in turn, yet another resource for poets. 66 When discussed, this early modern spurt of travel and trade networks has often been seen exclusively as the preserve of Europeans, their 'Age of Discovery', or some such. 67 But Asian traders, mystics and litterateurs were also extremely likely to travel over vast stretches of space, with almost no restrictions on their movement.…”

Section: Sabk-i Hindī and Philologymentioning

confidence: 99%

FRESH WORDS FOR A FRESH WORLD: TĀZA-GŪ'Ī AND THE POETICS OF NEWNESS IN EARLY MODERN INDO-PERSIAN POETRY

Kinra

2007

Sikh Formations

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This article examines a crucial phase of Indo-Persian literary modernity, beginning in the late sixteenth century CE, when poets and other literati across South, Central, and West Asia began articulating an unprecedented break with their cultural past through calls for 'speaking the fresh' (tāza-gū'ī). In later, nineteenth-and twentieth-century scholarship, this period of literary ingenuity has been almost universally decried as decadent and unworthy of serious study, an indictment that has, over the years, become specifically and explicitly coded in terms of India's allegedly debilitating effect on Persian language and literature. Thus in scholarly parlance this era is regularly (and pejoratively) referred to as that of the 'Indian Style' (sabk-i hindī), despite the fact that the early modern poets themselves never used such metageographical terminology, and despite the tāza-gū'ī movement's incontrovertibly transregional reach and cosmopolitan tenor. To interrogate this conceptual slippage, this article historicizes some key factors in the twentieth-century formulation of the notion of sabk-i hindī, and then contrasts them with evidence from a case study of the celebrated Mughal munshī and litterateur, Chandar Bha¯n Brahman (d. 1672 -3), whose sense of literary possibility and the interconnectedness of the early modern world are clearly at odds with the nationalist frames of later Iranian (and even Indian) thinkers. After using Chandar Bha¯n's example as a barometer for calling into question much of the modernist discourse about Safavid-Mughal literary and political culture, I offer a brief pre´cis of some suggestive comparative possibilities that could open up if we were to abandon the anachronistic sabk-i hindī model and return our attention to the poetics of ingenuity and 'freshness' (ta¯zagī) that were of central concern to the early modern Indo-Persian literati themselves.

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Section: Sabk-i Hindī and Philologymentioning

confidence: 99%

FRESH WORDS FOR A FRESH WORLD: TĀZA-GŪ'Ī AND THE POETICS OF NEWNESS IN EARLY MODERN INDO-PERSIAN POETRY

Kinra

2007

Sikh Formations

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“…Functionals of this type arise in problems akin to H ¥ /H p control; cf. Subrahmanyam (1995). We can expand the denominator in (1.4) as ,y(t),u(t) …”

Section: Introductionmentioning

confidence: 99%

Multi-time dynamic programming and Riccati equations

Belbas¹

1998

International Journal of Control

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This paper introduces a new type of dynamic programming equations for optimal control problems with performance criteria involving multiple integrals. The main novel feature of the multi-time dynamic programming equations, relative to the standard Hamilton± Jacobi equation, is that they form a Goursat± Darboux problem (i.e. boundary data are needed on two lines, or on planes or hyperplanes), whereas Hamilton± Jacobi equations form a Cauchy problem (initial value problem). In the case of performance criteria involving multiple integrals with quadratic integrands, the new equations lead to multi-time variants of the Riccati equation.

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“…This problem is motivated by engineering systems that follow a finite‐time trajectory and for which model uncertainty is a significant factor. Examples of such systems include: aircraft landings, 1 missile interceptors, 2 and space‐launch or reentry systems 3‐5 . The Jacobian linearization of the nonlinear dynamics along the trajectory yields an uncertain, finite horizon LTV system.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed algorithm, presented in Section 4, iterates between a nominal synthesis step and robustness analysis step. The nominal synthesis step relies on existing finite horizon H ∞ synthesis results which consider a control theoretic formulation 1,10‐12 . An alternative game theoretic formulation is considered in Reference 13 which provides equivalent synthesis conditions.…”

Section: Introductionmentioning

confidence: 99%

Finite horizon robust synthesis using integral quadratic constraints

Buch

Seiler

2021

Intl J Robust & Nonlinear

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We present a robust synthesis algorithm for uncertain linear time‐varying (LTV) systems on finite horizons. The uncertain system is described as an interconnection of a known LTV system and a perturbation. The input–output behavior of the perturbation is specified by time‐domain Integral Quadratic Constraints (IQCs). The objective is to synthesize a controller to minimize the worst‐case performance. This leads to a nonconvex optimization. The proposed approach alternates between an LTV synthesis step and an IQC analysis step. Both induced ℒ2 and terminal Euclidean norm penalties on output are considered for finite horizon performance. The proposed algorithm ensures that the robust performance is nonincreasing at each iteration step. The effectiveness of this method is demonstrated using numerical examples.

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Finite Horizon H∞ and Related Control Problems

Cited by 11 publications

References 0 publications

FRESH WORDS FOR A FRESH WORLD: TĀZA-GŪ'Ī AND THE POETICS OF NEWNESS IN EARLY MODERN INDO-PERSIAN POETRY

FRESH WORDS FOR A FRESH WORLD: TĀZA-GŪ'Ī AND THE POETICS OF NEWNESS IN EARLY MODERN INDO-PERSIAN POETRY

Multi-time dynamic programming and Riccati equations

Finite horizon robust synthesis using integral quadratic constraints

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